Abstract
Calibration consists of using a fitted regression line to estimate the value of an unobserved independent variable x corresponding to an observed dependent variable y. To construct a confidence interval for a single x, Eisenhart introduced a procedure that consists of inverting prediction intervals around the regression line. Numerous other inference procedures have been proposed for multiple-use calibration, in which a single fitted regression line is used repeatedly to estimate many x's, We provide a synthesis of this literature and offer some numerical comparisons. We also attempt to motivate the use of various criteria based on the particular points of view of the various parties involved in determining the calibration or using the results. In addition, we derive probability expressions for computing exact simultaneous prediction intervals that enable the construction of tighter limits than are currently available based on that criterion.
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